The aim of the present paper is to provide an intrinsic investigation of special Finsler spaces of Hp-scalar curvature and of Hp -
constant curvature. Characterizations of such spaces are given. Sufficient
condition for Finsler space of Hp-scalar curvature to be of perpendicular
scalar curvature is investigated. Necessary and sufficient condition under
which a Finsler space of scalar curvature turns into a Finsler space of
Hp
-scalar curvature is shown. Further, certain conditions under which a
Finsler manifolds of H
p-scalar curvature and of scalar curvature reduce
to a Finsler space of Hp-constant curvature are obtained. Finally, various
examples are studied and constructed.